Some charity shops will still take them, or you could try the Oxfam Bookshop (our local branch will also take LPs, CDs, DVDs & VHS tapes).
By the way, Boots allegedly have a recycling scheme for blister packs (those little plastic pop-out trays that hold pills). Not every branch takes them, though, so I'll believe it when I see it.
Our local Co-Op, in spite of being specifically listed online as having a recycling box for plastic bags, bread bags, crisp packets, etc. When I took mine in, nobody had even heard of the scheme, much less had a box for the purpose!
I think a lot of these schemes exist more as ticked boxes in the publicity departments of big companies, rather than real places where you can take your recycling. Plastics may be recyclable in theory but, unless someone actually does recycle them (rather than just taking them off the consumers' hands), the planet is effectively still stuck with them.